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Lecture 28: Transition Metals: Crystal Field Theory Part I

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Lecture 28: Transition Metals: Crystal Field Theory Part I 5.111 Lecture #28 Wednesday, November 19, 2014 Reading For Today: 16.8-16.11 in 4th and 5th editions Reading for Lecture #29: same as above Topic: I. Introduction to Crystal Field Theory II. Crystal Field Theory: Octahedral Case III. Spectrochemical Series I. Introduction to Crystal Field Theory Crystal field and ligand field theories were developed to explain the special features of transition metal coordination complexes, including their beautiful colors and their magnetic properties. Coordination complexes are often used as contrast agents for magnetic resonance imaging (MRI) and other types of imaging. Basic idea behind theories: When a metal ion with a given oxidation number (Mn+, where M is a metal and n+ is its oxidation number) is placed at the center of a coordination sphere defined by a set of ligands, the energy levels of the d orbitals housing the metal electrons are from those in the free metal ion. Crystal field theory is based on an ionic description of the metal-ligand bond. Ligand field theory includes covalent and ionic aspects of coordination. It is a more powerful description of transition metal complexes. It is, however, beyond the scope of this course. (Take 5.03 if you are interested in this topic). Crystal Field Theory considers ligands as point charges and considers the repulsion between the negative point charges and the d-orbitals, and even though this theory is simple, a number of properties of transition metals can be explained. L- L- L- Mn+ L- - L L- © W.H.Freeman & Co Ltd. All rights reserved. This content is excluded from our Creative Commons license. For more information, see https://ocw.mit.edu/help/faq-fair-use/. 1 II. Crystal Field Theory: Octahedral Case L- - Z L Z L- Mn+ L- Y Y X X L- - L 2 2 d - x y 2 dz 2 2 2 • Ligand (L) point charges are directed right toward the dz and dx -y orbitals of metal (Mn+), resulting in a large repulsion. 2 2 2 • The dz and dx -y orbitals are destabilized, and they are destabilized by the same 2 2 2 amount. dz and dx -y are . 2 2 2 • The dz and dx -y orbitals are destabilized relative to dxy, dyz , and dxz. Z Z Z L- L- - n+ L- L M Y Y Y X X X L- L- dyz dxy dxz • Ligand point charges are directed in between dxy, dxz, and dyz orbitals (not directly toward them), resulting in repulsion. 2 2 2 • The dxy, dxz, and dyz orbitals are stabilized relative to dz and dx -y orbitals, and they are stabilized by the same amount. • dxy, dxz, and dyz orbitals are degenerate with respect to each other. 2 Octahedral Crystal Field Splitting Diagram 2 2 2 label for degenerate dx -y and dz orbitals (eg) 2 2 d 2 dx -y z + 3 O O 5 - 2 O average energy of d orbitals with 5 ligands (t ) dxy d d 2g (Spherical crystal field) xz yz (Octahedral crystal field) label for degenerate dxy, dxz, dyz orbitals ∆o is the overall splitting between eg and t2g orbitals = octahedral field splitting energy ("o" in ∆o is for octahedral) Because the overall energy is maintained, the energy of the three t2g orbitals are lowered by (2/5) ∆o and the energy of the two eg orbitals are raised by (3/5) ∆o relative to the spherical crystal field. What determines the magnitude of ∆o ? Answer: the _____________of the ligand. III. Spectrochemical Series The relative abilities of common ligands to split the d-orbital energy levels generate what is known as the spectrochemical series. Strong field ligands - produce energy separations between d-orbitals (big ∆o) Weak field ligands - produce small energy separations between d-orbitals (small ∆o) - - - - - - I < Br < Cl <F < OH < H2O <NH3 < CO < CN weak field ligands strong field ligands ∆o is small ∆o is large 3+ 3- Example 1. Consider two different iron compounds: [Fe(H2O)6] and [Fe(CN)6] . (a) Figure out the oxidation number of Fe (b) Figure out d count 3 (c) Draw octahedral crystal field splitting diagrams Small Δo (______________field) Large Δo(______________fiel d) (e ) 2 2 d 2 g (eg) dx -y z 2 2 2 + 3 O dx -y dz + 3 O 5 5 O O - 2 - 2 5 O O (t2g) (t 5 d 2g) dxy dxz yz dxy dxz dyz Compound is Compound is (d) Place electrons. There are two ways to place electrons: (1) singly to the fullest extent possible before pairing (i.e. using both t2g and eg orbitals) or (2) only fill t2g before pairing. The decision is made based on whether Δo is greater or less than the pairing energy (PE): energy of electron-electron repulsion. When ∆o is small, ∆o < PE When ∆o is large, ∆o > PE Electrons are placed singly with parallel Electrons are paired in lower energy spins to the fullest possible extent in t2g orbitals. eg orbitals are not both t2g and eg orbitals. occupied until t2g orbitals are filled. This arrangement of electrons gives This arrangement of electrons gives the maximum number of unpaired the minimum number of unpaired electrons (high spin). electrons (low spin). (e) Write dn electron configuration: (f) Predict Crystal Field Stabilization Energy (CFSE) - relative to that of the hypothetical spherical crystal. CFSE = Practice Questions (eg) 2+ 7 (e ) + 3 1. Place electrons correctly for an octahedral Co (d ) g O d 2 2 d 2 x -y z + 3 O 5 weak field complex. O 5 O - 2 - 2 O O 5 5 (t2g) (t2g) dxy dxz dyz dyz 3+ 3+ Cr3+ in [Cr(NH ) ]3+ Cr in [Cr(H2O)6] 3 6 4 (eg) (eg) + 3 O 2. Predict the CFSE of a high spin octahedral d 2 2 d 2 3+ 4 x -y z + 3 O 5 Mn (d ) complex 5 O - 2 - 2 O O 5 5 (t2g) (t2g) dxy dxz dyz 3+ 3- Back to [Fe(H2O)6] and [Fe(CN)6] 3+ 3+ Cr3+ in [Cr(NH ) ]3+ Cr in [Cr(H2O)6] 3 6 Predict whether these compounds are paramagnetic (attracted by a magnetic field) or diamagnetic (repelled by a magnetic field). Based on the above diagrams, they are likely to be____________________(i.e. have electrons). Predict the colors of these two iron complexes Light Absorbed and Emitted by Octahedral Coordination Complexes A substance absorbs photons of light if the energies of the photons the energies required to excite the electrons to higher energy levels. Elight = hν = ∆o E = energy of light absorbed; h = planck's constant ν = frequency; ∆o = octahedral crystal field splitting energy If low frequency light is absorbed, the wavelength of the absorbed light is . (yellow/orange/red end of spectrum) If high frequency light is absorbed, the wavelength of the absorbed light is . (violet/blue/green end of spectrum) c=λν c = speed of light λ = wavelength ν = frequency violet blue green yellow orange red | | | | | | | λ 400nm 430nm 490nm 560nm 580nm 620nm 800nm Color of transmitted light is to the col or of absorbed light. 3+ 3- Going back to our example: high spin [Fe(H2O)6] and low spin [Fe(CN)6] 3+ High spin [Fe(H2O)6] absorbs low frequency/long wavelength light and transmits wavelength light. It can appear pale violet to yellow brown. 3- Low spin [Fe(CN)6] absorbs high frequency/short wavelength light and transmits wavelength light. It is bright red-orange. 5 Which coordination complexes are colorless? All d-orbitals are . d-d transitions in the visible range possible. Examples: Will Co3+ be colorless? Which vitamin contains cobalt? Cobalt Flower Demonstration 2+ Predict the color of [Co(H2O)6] (∆o = 239 kJ/mol) (a) Calculate the wavelength of absorbed light -34 8 λ = hc/∆o = (6.626 x 10 J s) (2.997 x 10 m/s) = (239 kJ/mol)(1000 J/kJ)(1 mol/6.022 x 1023) 2+ [Co(H2O)6] absorbs _____________ light. (b) Predict the color of the transmitted light . 2+ In solution, CoCl2 + H2O -> [Co(H2O)6] color = In the solid state, CoCl2 + H2O –> trans-[CoCl2(H2O)4] color = blue So we can go between and blue by adding water (hydrating) or removing water (dehydrating). 6 MIT OpenCourseWare https://ocw.mit.edu 5.111 Principles of Chemical Science Fall 2014 For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms..
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